Train Travel out of Heathrow

No trains direct from Heathrow to Bath (actually the station is called Bath Spa). You would have to take either the Heathrow Express or Heathrow Connect train from Heathrow to Paddington Station in London and get a train from there to Bath Spa. Heathrow Express is quicker (15 mins) but more expensive than Heathrow Connect (30 mins.) You could also take a coach (bus) from the Central Bus Terminal located at Heathrow (between T1 and T3) to Bath. It's slower than the train and runs less frequently but is cheaper. National Express: http://www.nationalexpress.com There are some other combinations of options like a coach to Reading, and catch the train to Bath. I'm planning this myself right now. I arrive at 4:45 pm and don't actually need to be in Bath till the next afternoon. So I decided to stay overnight in London, catch a show in the West End, get a good night's sleep to put a dent in the jet lag, then catch the earliest train the next morning to Bath.

Thanks. We played around with the train site a little more and were able to do the Heathrow express to Paddington and then take a train to Bath. We have just found the websites to be a bit frustrating. We are getting in early in the morning so will be taking it slow in Bath while we recover. Paddington was on the list so it all worked out.
Have a great time!

From terminal 5 there is no time benefit in taking the Heathrow Express to Paddington, over taking the coach to Reading - and the latter will be much cheaper.

Marco is correct, as always. The coach service from Heathrow to Reading railway station is called RailAir and its website is http://www.railair.com/ An off-peak ticket from Reading to Bath Spa is about 25% cheaper than a similar ticket from London Paddington, on the same trains. Going into London to catch it means doubling back on yourself.